Question: Rewrite as a simplified fraction. ${1.\overline{32} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 132.3232...\\ 1x &= 1.3232...\end{align*}}$ Subtracting the two equations, we have: ${99x = 131}$ ${x = \dfrac{131}{99}} \text{or} {1 \dfrac{32}{99}}$